nativ3 0.2.0

Topology-aware quantum compiler using universal transfer matrices (24 theorems, 42K+ tests, 0 failures)

Nativ3 — Topology-Aware Quantum Compiler

24 theorems. 42,000+ tests. Zero failures.

Quantum circuit topology and classical network topology are the same mathematical object, connected by a universal 4×4 transfer matrix with bond dimension 4 = 2⊗2.

Install

pip install nativ3
pip install nativ3[qiskit]  # with Qiskit integration

Quick Start

from nativ3 import compile_circuit

# Define your circuit as (control, target) pairs
circuit = [(0,1), (0,2), (0,3), (1,2), (2,3)]

# Define hardware connectivity
hardware = {0:[1], 1:[0,2,4], 2:[1,3], 3:[2,4], 4:[1,3]}

# Calibration data (from IBM Quantum)
calibration = {
    "qubits": {q: {"gate_fidelity": 0.998} for q in range(5)},
    "edges": {(i,j): {"cx_fidelity": 0.97} for i in range(5) for j in hardware.get(i,[])}
}

# Compile: finds optimal qubit mapping maximizing topology cost Z
mapping, Z, swaps = compile_circuit(circuit, hardware, calibration)
print(f"Optimal mapping: {mapping}")
print(f"Topology cost Z: {Z:.4f}")
print(f"SWAP gates needed: {swaps}")

What Z Captures That SWAP Count Doesn't

• Per-qubit fidelity (not all qubits are equal)
• Per-edge CX fidelity (not all connections are equal)
• Chain length effects (longer chains decay nonlinearly)
• Hub structure (star circuits prefer high-connectivity nodes)
• Multi-gate optimization (different transfer matrix per gate type)

Among mappings with the same SWAP count, Z discriminates by up to 35%.

Key Results

Theorem	Result
T1-T2	Non-transitivity of CU topology, F = cos⁴(α)
T15-T16	Universal 4×4 transfer matrix, bond dimension 4
T17	Projector angle: det(M) = 0, classical stochastic matrix
T19	Relay = eigenvector of gate at projector
T22	Self-referential: M is itself a CU gate
T23	Novelty formula with conservation law
T24	Deflection D² = 1-Z², breathing ratchet

Links

• Paper: doi.org/10.5281/zenodo.19302455
• IDE: nativ3.shift8.space
• Breathing Mode: breathing.shift8.space